Angle D is 180° -75° -45° = 60°. Drawing altitude MX to segment DN divides the triangle into ΔMDX, a 30°-60°-90° triangle, and ΔMNX, a 45°-45°-90° triangle. We know the side ratios of such triangles (shortest-to-longest) are ...
... 30-60-90: 1 : √3 : 2
... 45-45-90: 1 : 1 : √2
The long side of ΔMDX is 10√3, so the other two sides are
... MX = MD(√3/2) = 15
... DX = MD(1/2) = 5√3
The short side of ΔMNX is MX = 15, so the other two sides are
... NX = MX(1) = 15
... MN = MX(√2) = 15√2
Then the perimeter of ΔDMN is ...
... P = DM + MN + NX + XD
... P = 10√3 +15√2 + 15 + 5√3
... P = 15√3 +15√2 +15 . . . . perimeter of ΔDMN
If an integer is chosen between 1 and 50 inclusive, you have 50 numbers total to deal with, so 50 is in the denominator of our ratio (fraction). All the numbers divisible by 3 in that interval total 16 numbers. So the ratio would be 16/50 for a percentage of 32%
Why would they chose a dog at random?
You need to feel a connection.
(8.4−4.5)(7.04−0.04)
=3.9(7.04−0.04)
=(3.9)(7)
=27.3
Ans : 27.3
Answer:
The distance between (0,3) and (7,3) is 7
